This essay offers an overview of the theoretical and empirical research on taxevasion, delineating the variety of factors affecting noncompliance andexamining possible remedies. Particular emphasis is placed on the institutionaland procedural rules governing the tax enforcement policy.

Tax evasion is said to occur when individuals deliberately fail to comply withtheir tax obligations. The resulting tax revenue loss may cause serious damageto the proper functioning of the public sector, threatening its capacity to financeits basic expenses.

Although tax compliance is a major concern for all governments andanalytical investigation of tax evasion can be traced as far back as the work oneof the pioneers of "law and economics," Cesare Beccaria (1764) , the problem waslong segregated from the main body of economics and left essentially to theattention of tax authorities and jurisprudence. The modern use of economic toolsfor the analysis of tax compliance can be credited to Allingham and Sandmo(1972) , who extended the influential work of Becker (1968) on law enforcementto taxation using modern risk theory.

In the decades since, the literature on tax evasion has blossomed (aswitnessed by the voluminous bibliography enclosed). Probably no aspect of taxcompliance has escaped at least preliminary scrutiny. Detailed introductions tothis theme are now available, as in the monographs of Cowell (1990) (theoretically oriented) and Roth et al. (1989) (an interdisciplinary perspective),and the surveys of Andreoni, Erard and Feinstein (1998) (including a thoroughdiscussion of empirical results) and Slemrod and Yitzhaki (1998) (with largesections devoted to avoidance and administration).

As a complex phenomenon, tax compliance can be addressed from a varietyof perspectives. Taxpayers' stance is influenced by many factors, including theirdisposition towards public institutions, the perceived fairness of the taxes,prevailing social norms, and the chances of noncompliance being detected andpunished. Without questioning the relevance of ethical and sociologicalmotivations, the economic analysis of tax compliance has focused mainly onhow evasion can be deterred through detection and sanctions. The thesis is thatthe taxpayer's behavior can be fruitfully seen as the result of a rational calculus,a careful assessment of the costs and benefits of evasion. Since even in thesimplest tax and enforcement systems the incentives to comply are far fromobvious, this economic perspective offers precious insights that can be used toderive suitable policy measures. Yet, given the complexity of the economicset-up in which the taxpayer usually makes compliance decisions, no simplepolicy prescription should be expected. In fact, as we will see, to date theoreticaland empirical research has managed to establish very few firm points.Nevertheless, the general picture of tax compliance is much clearer now than justa few decades ago. At least the literature has shown that evasion is a seriousproblem, too complex to be solved by simple policy adjustments, and that the setof instruments for controlling it is vast.

By distancing effective payments from statutory taxes, tax evasion defines aspecific revenue deficiency, known as the "tax gap." (In the US, for example, thefederal income tax gap has been estimated at 17%).

Let us emphasize from the outset that the tax gap is not equal to the amountof additional revenue that would be collected by stricter enforcement. For perfectenforcement would significantly affect the economic scenario (some firms wouldgo bankrupt, taxpayers would modify their labor supply, prices and incomeswould change, etc.), so the tax base would surely be altered. As a result, at leastin theory, net revenue could even turn out to be smaller. Thus standardmeasures of tax gaps must be interpreted cautiously. They are only roughlysuggestive of the likely immediate effects of marginal improvements inenforcement. Also, one should be wary of the cliché that statutory taxesrepresent the ideal world and tax gaps an intrinsic evil. This is not only becausetaxes may not be "just", but also because statutory taxes themselves are usuallydetermined by a legislature that is perfectly aware that they will only be partiallyenforced and therefore differ from those that would be optimal under perfectenforcement.

On closer scrutiny, therefore, estimation of the tax gap merely portrays thewedge between economic reality and a purely legal construct called "statutorytaxes." Reality and its legal representation may differ for any number of reasons,among which, as we shall see, the willful misrepresentation of tax liabilities is justone.

In economic terms, evasion problems originate in the fact that the variablesthat define the tax base (incomes, sales, revenues, wealth, etc.) are often not"observable." That is, an external observer cannot usually see the actualmagnitude of an individual's tax base, and hence cannot know his true taxliability. Sometimes this knowledge can be obtained by means of costly audits,in which case we say that the tax base is verifiable (at a cost). In other cases, aswhen it is related to cash payments, the tax base cannot be verified at all.Taxpayers can take advantage of the imperfect information about their liabilityand elude taxation.

A related concept is tax avoidance (or reduction), by which individualsreduce their own tax in a way that may be unintended by tax legislators but ispermissible by law. Avoidance is typically accomplished by structuringtransactions so as to minimize tax liability. In some cases, avoidance isencouraged by legislation granting favorable tax treatment to specific activitiesin contrast to general taxation principles. From a legal standpoint, evasion differsfrom avoidance in being unlawful, and hence punishable (at least in theory). Asfar as economic function is concerned, however, evasion and avoidanceobviously have very strong similarities; sometimes, indeed, they can hardly bedistinguished [see for instance Feldman and Kay (1981) , Cowell (1990) , and McBarnet (1992) ]. This adds to the difficulty of interpreting the real implicationsof the tax gap.

Another problem with the measurement of tax evasion relates to its properdelimitation within the broader set of the informal economy. No taxes aregenerally levied on transactions in the home and criminal sectors, which areusually beyond the reach of authorities and official statistics. Hence, properdetermination of the boundaries of evasion is a formidable task, in that evasionis often inextricable from other illegal and unrecorded activities. What, one mightask, is the evaded tax of a hired killer?

Aggregate estimates of evasion must deal with all these problems, in additionto the classic problem of lack of direct data. Various estimation methods havebeen devised, some based on data collected by fiscal authorities, others - lessreliable - on data derived from national accounts and surveys. Their applicationsuggests that in the Western industrialized countries evaded taxes amount tobetween 5% and 25% of potential tax revenue, depending on the techniqueadopted and the country [see monographs by Feige (1989) , Pyle (1989) and Thomas (1992) ], with higher figures (up to a 30-40%) for less developedcountries [ Tanzi and Shome (1994) ].

As noted, one should not attach too much importance to such estimates,which essentially tell us that statutory taxes are not the whole story. Whatmatters is effective taxation , i.e. the net tax burden on individuals. This has majorimplications bearing on the economic consequences of evasion: the mainquestion is not how evasion alters the shape of statutory allocation of the fiscalburden, but how it constrains the set of policies that can be implemented. Whentaxes can be evaded, taxation will prove to be an imperfect tool for pursuinggovernment aims (be they redistribution, efficiency, or whatever), which will beonly partly achieved. Indeed, effective taxation may turn regressive, as the moreaffluent usually have better opportunities to evade (or avoid) taxes. Also,evasion may be powerfully deleterious to horizontal equity, owing to unequaldistribution of opportunities to evade and of the willingness to seize them. Thisin turn may induce production inefficiencies, because competition would bedistorted by the unequal distribution of the tax burden among firms.

The adverse consequences of tax evasion are sometimes exacerbated bylaws, or even constitutions, drafted as if the tax base were observable, limitingthe set of corrective instruments available to the government (which cannot, forinstance, set tax rates according to their presumed degree of enforceability).

In order to evaluate the way in which noncompliance affects the actual taxpayment of individuals, one must examine taxpayers' compliance behavior moreclosely. This can be done by developing a theoretical model to predict howtaxpayers' behavior is affected by the relevant variables. The following sectionreviews some models and assesses their fit with observed practise.

Compliance with the tax law typically means: i) true reporting of the tax base, ii)correct computation of the liability, iii) timely filing of the return, and iv) timelypayment of the amounts due. The bulk of tax evasion involves the first point.Most evaders either do not declare their liability at all, or declare it only in part.In the following, we concentrate on the problem faced by an individual who hasto decide how much of his tax aggregate to report, or whether to report it at all.The focus is on income taxes (which account for a large part of fiscal revenue inmost countries). However, the insights provided can be applied to other taxesas well.

3.1 Allingham and Sandmo

A useful model of taxpayers' evasion decision is that developed by Allinghamand Sandmo (1972) and Srinivasan (1973) , and revised by Yitzhaki (1974) .Evasion is viewed as a portfolio allocation problem: the taxpayer must decidewhat portion of his income y (postulated as exogenous) to invest in the riskyactivity labeled "tax evasion." If the taxpayer does not want to take any risk, hereports his income in full; otherwise, he reports only a fraction of it and bears therisk of being caught and fined. The problem is thus to choose the optimal taxreturn, when the income reported is taxed at a fixed rate t and evasion is fined ata penalty rate f proportional to the tax evaded. The probability of an audit, i.e.the probability that the true income level will be discovered, is a constantdenoted by a . The taxpayer decides the amount to conceal so as to maximize hisexpected utility from net income. If we call y NA the net income when the evaderis not audited (gross income less taxes on reported income) and y A the netincome when he is audited (gross income less taxes on true income less the fine),we can write the taxpayer's expected utility as

This representation yields some interesting results from the standpoint ofcomparative statics. On the reasonable assumption that the taxpayer isrisk-averse, it can be shown that the amount of tax evaded, te * , varies inverselywith the audit rate a and the penalty rate f , while it depends negatively on the taxrate t and positively on income y if and only if taxpayer's utility functiondisplays Decreasing Absolute Risk Aversion. Further, the proportion of taxevaded, te * /y , increases with income if and only if taxpayer's utility functiondisplays Decreasing Relative Risk Aversion [see Cowell (1990) ]. Of these results,the least obvious is surely the inverse correlation between the amount ofevasion and the tax rate (with DARA). This stems from the fact that both thedirect gain from evasion (taxes saved) and the expected fine dependproportionally on t . Hence, an increase in the tax rate does not induce the"substitution" of the risky asset for the safe one, but operates solely throughthe reduction in disposable income [ Yitzhaki (1974) ].

Once the optimal amount of underreporting, e* , has been calculated, one caneasily derive the "evasion rent," defined as the monetary benefit accruing to theevader (more precisely, the amount of income that he would be willing to pay toswitch from a virtual system of perfect enforcement to the actual, imperfect, one):

Evasion rent = [1 - a (1 + f )] te* - RP ( e* ),

where RP ( e* ) is the risk premium associated with the audit lottery. The evasionrent is therefore equal to the net return on evasion (evaded taxes less expectedsanctions) less the "loss" due to the riskiness associated with random auditing(note, incidentally, that if taxpayers were risk-lovers, the risk premium wouldeffectively represent a "gain").

Several observations are in order. First, for evasion rent to be positive, thenet return on evasion has to be positive (the evasion gamble needs to be "betterthan fair"). That is, for evasion to occur at all, it is necessary that a (1+ f )<1; i.e.the penalty and audit rates must be sufficiently low. Second, when the net returnon evasion is positive, the only reason why taxpayers may not evade their wholetaxes is the fear of uncertainty (the risk premium loss). Indeed, if taxpayers wereinfinitely averse to risk, they would report their income in full even if the netreturn on evasion were positive (taxpayers are hyper-pessimists and behave asif they were to be audited for sure). Finally, the risk premium produces adifferential between the rent to the taxpayer and the net revenue loss to the taxauthorities. Hence, it provides a monetary measure of the "deadweight loss" dueto the randomness of tax enforcement [ Yitzhaki (1987) ].

3.2 Extensions

This basic model gives an account of taxpayers' evasion decisions in a verysimple set-up: taxes and penalties are proportional, the audit rate is constant,only one form of evasion is available. In addition, the taxpayer is assumed to relyon expected utility theory and to be perfectly amoral, i.e. to make compliancedecisions with exclusive reference to the consequences for net income. All theseassumptions are open to criticism, and models based on alternative assumptionshave been developed. The following touches briefly on these contributions.

One standard criticism of the Allingham and Sandmo model is grounded inthe belief that compliance decisions depend on moral views. This is clearly aproblematic issue, one that cannot be captured by the consequentialistic set-upof standard decision theory. Bordignon (1993) makes an interesting attempt toaccount for non-self-motivated decisions in tax evasion. He develops acompliance model in which taxpayers are guided by suitably defined "Kantianprinciples," which determine the amount that each taxpayer considers fair to pay.Under this assumption, it turns out that tax evasion is generally lower than underselfish behavior, that compliance depends on the level of public expenditure,and that evasion is likely to increase with tax rates.

Other authors have stressed the "social" factors at the basis of taxpayers'decision [see Roth et al. (1989) for an excellent account of the sociologicalresearch]. Economists have emphasized the "stigma" attached to the violationof social norms and shown that tax evasion may have strong spill-over effects.Social stigma is likely to give rise to a multiplicity of possible equilibria: whenmost people evade, the stigma effect is small and evasion is not in factdiscouraged; when few evade, the stigma effect is great and evasion isdiscouraged. The transition from one equilibrium to the other takes the form ofa "noncompliance epidemic:" if, for some reason, more people start to evade, thestigma decreases and evasion spreads to an ever larger fraction of thepopulation [see Benjamini and Maital (1985) , Gordon (1989) and Myles andNaylor (1996) ].

Scotchmer and Slemrod (1989) and Scotchmer (1989) consider the effect ofrandomness in tax liability assessments. Among other things, both papersconclude that uncertainty over the true liability level or outcome of the auditincreases net tax revenue, either because increased uncertainty makes evasionmore costly (when taxpayers are risk-averse) or because it may lead taxpayers tounder-report their income and be subject to a fine (whereas over-reporting onlyyields a rebate of the overpaid tax).

Several authors have tried to extend Allingham and Sandmo's model toinclude the labor supply decision, so as to endogenize taxpayers' gross income[see, among others, Andersen (1977) , Pencavel (1979) , Isachsen and Strom(1980) , Isachsen, Samuelsen and Strom (1985) , and Cowell (1985) ]. The problemis that as soon as the labor decision is factored in, the simple comparative staticsof Allingham and Sandmo are lost. Depending on the taxpayer's marginaldisutility from labor and her risk-attitudes, all predictions become possible. Thisproblem is usually overcome by imposing strong restrictions on the utilityfunction. Cowell (1985) takes a different course, assuming that decisions aremade in two separate stages: first, the taxpayer decides how many hours towork; then he allocates this total labor supply between legal and illegal activities(alternatively, between reported and unreported income). On this assumption,Cowell is able to show that Allingham and Sandmo's results carry over (withsome qualifications) to the extended set-up if taxpayer's labor supply is forwardrising. Perhaps more importantly, he shows that the comparative statics resultsare strictly dependent on the nature of the evasion choice, as it can be tied eitherto the amount of income to report (for the self-employed) or to the amount oftime to spend in "off the books" activities (for the moonlighter).

The insights drawn from analysis of income tax evasion usually apply toother forms of evasion as well. Different considerations may be relevant,however, when the taxpayer is a firm subject to indirect taxation, as the evasiondecision may affect output or pricing policy (tax shifting). However, Marrelli(1984) derives a separability result for the case of a monopolist: the evasion andshifting decisions are independent of one another as long as the auditprobability is constant [see also Yaniv (1995) ]. The same result applies tooligopolistic markets when firms compete à la Cournot [ Marrelli and Martina(1988) ]. Here, the amount of evasion by each firm is shown to depend, apart fromthe enforcement parameters, on the degree of collusion and on market shares.

Gordon (1990) offers an interesting insight on sales tax evasion. He suggeststhat under-the-counter cash sales may serve as a means of price discrimination:cash discounts are the best pricing strategy when the demand for cashpurchases is highly elastic. The author also shows that, in order to reduce cashsales, a liability on detected cash customers could be imposed, but on thecondition that this is an additional liability, and not just a transfer of a part ofthe supplier's existing liability onto the consumer.

As is clear form the foregoing, taxpayer noncompliance decisions may bevery complex and are likely to be powerfully affected by the practical frameworkin which decisions are made. This thesis is strongly supported by the empiricalevidence, which we now briefly review.

Evidence on taxpayers' behavior is notoriously difficult to come by. Data on theextent of evasion may be confidential (not available for external analysis) or notcompletely reliable (such as those derived from national accounting sources). Allthe same, empirical studies on the determinants of taxpayers' compliancedecisions have proliferated. The most detailed are based on the AmericanTaxpayer Compliance Measurement Program (TCMP), conducted regularly bythe IRS and based on a "line by line" audit of a sample of 45,000 to 55,000 taxreturns. In addition to statistical estimates, major insights on the dynamics ofcompliance have been obtained from questionnaires and experimentation.

In his pioneering analysis, Clotfelter (1983) uses TCMP data for 1969 toinvestigate the determinants of underreporting, which is defined as thedifference between the income reported and that assessed by IRS examiners. Hefinds that both the marginal tax rate and after-tax income have significant effectson individual underreporting. In contrast to Allingham and Sandmo's prediction,he finds that elasticities with respect to marginal tax rates are positive and rangefrom 0.5 for non-farm business to 0.8 for non-business returns. In line withAllingham and Sandmo, elasticities with respect to after-tax income are positiveand range from 0.3 for non-business returns to 0.65 for farm returns. Also,wages, interest and dividends are associated with better compliance andunderreporting is higher for the youngest age-groups. Witte and Woodbury(1985) also analyze data from the TCMP for 1969, but focus on the effect ofenforcement parameters. They find that the percentage of underreporting isrelated inversely to the probability of audit (with a lagged effect), and directlyto the "opportunities" for tax evasion (absence of withholding and informationreporting) and to income, though in a decreasing way. Dubin and Wilde (1988) criticize Witte and Woodbury's results and highlight the potential endogeneityof audit rates. The idea is that audit rates are decided by the IRS in view of theirpotential yield: a decrease in noncompliance rates reduces the net return fromauditing and leads the IRS to devote less effort to auditing. Using the IRSbudget per return as an instrumental variable for the audit rates, they find theaudit rate to be endogenous in 5 out of 7 audit classes. They also find thataudits have a deterrent effect on evasion, and that noncompliance is positivelyrelated to the unemployment rate and the nonwhite fraction of the population. Feinstein (1991) uses a sophisticated estimation technique, which allows forpartial detection by IRS examiners. His results confirm the great unevenness incompliance attitudes between groups of taxpayers, with "own business" and"farm" filers scoring the lowest compliance rates. Using TCMP data for 1982 and1985, Feinstein more easily disentangles the effects of marginal tax rates andgross income (taxpayers with identical incomes filing in different years facedifferent marginal tax rates). He finds that the effect of marginal tax rates onevasion is negative and highly significant, while the effect of income isessentially zero. The former finding is consistent with Allingham and Sandmo'spredictions, while the latter is not. Another finding is that greater propensity toevade is accompanied by a higher detection rate (thanks to greater IRSexamination effort).

Studies based on IRS data provide a picture of the compliance phenomenonin which many factors come into play: income source, socioeconomic grouping(age, sex, location), detection probability, marginal tax rate and income level.Notably, the severity of the sanction does not seem to play a significant role(partly because in the US sanctions are rarely inflicted). Estimates based on IRSdata, however, are subject to several weaknesses. First, by definition, TCMPprograms relate to filers only, whereas in 1976, for example, strategic non-filersaccounted for an estimated 36% of all unreported income. In addition, it is wellknown that IRS examiners have only limited capacity to detect evasion,especially on income from moonlighting and cash-only businesses. Finally,strong assumptions underlie the choice of instruments and variables asexogenous regressors.

Survey studies face several problems, however. First, results dependcrucially on the representativeness of the sample, which is often difficult toassess. Second, respondents are reluctant to report acts of noncompliance [see,for instance, Elffers, Weigel and Hessing (1987) ]. Third, causal relationships aredifficult to establish. The finding that respondents who perceive the highestprobability of detection are most compliant, for instance, is consistent both withthe standard "deterrence hypothesis" and with the "experiential hypothesis"whereby taxpayers initially overestimate detection probabilities and evaders laterlower their estimates if they are not detected [ Saltzman et al. , (1982) ]. Finally,individuals often seek to provide a consistent image of themselves, offering adhoc rationalizations for their behavior [ Elffers, Weigel and Hessing (1987) ].

A third, increasingly widespread empirical approach is based on "laboratory"experiments [see, for instance, Baldry (1987) , Webley et al. (1991) , Alm,Cronshaw and McKee (1993) , Alm, Jackson, and McKee (1993) , and Alm,Sanchez and de Juan (1995) ]. Individuals (often students) are asked toparticipate in games simulating tax compliance, where they can underreport andincur the risk of a penalty. At the end, they receive a real reward proportional totheir laboratory performance. The results tend to be very sensitive to theparticular design of the experiment. In general, this research suggest that auditrates may play an important role in compliance decisions (especially for thosewho have already been audited), and that compliance is an increasing functionof income and a decreasing function of the tax rate, while it is hardly affected bythe size of fines (unless the audit rate is very high). These experiments alsosuggest that social norms and ethical attitudes play an important part in evasionchoices, that individuals often take an all-or-nothing stance, that they tend tooverweight low probabilities, and that the structure of the taxes is important[ Baldry (1987) ].

While the empirical research is far from conclusive, it does appear to supportthe hypothesis that expected punishment (i.e. the size of sanctions discountedby the probability of incurring them) is relevant. Sociological and ethical factorssurely play an important role too, although their effect is subtler and harder tomeasure. This suggests that standard enforcement polices based onapprehension and punishment should not be abandoned. They could besupplemented by alternative approaches, seeking to appeal to taxpayers' moralconscience or to reinforce social cohesion.

The following section treats the question of optimal design of taxenforcement policy, focusing on detection and punishment of evaders.

Let us go back to the model of Allingham and Sandmo. While it provides a fairlysophisticated description of taxpayers' evasion decisions, it leaves very littlescope for enforcement policy. The latter is essentially reduced to twoparameters: the penalty rate and the audit rate. The main policy prescriptionimplicit in the model and most of its variants is that, in order to curb evasion,audits have to be stepped up and fines increased. And given that raising theaudit rate is likely to require public resources while an increase in the penaltyrate is not, the end result is likely to be one with Draconian but rare punishment,a rule such as " hang evaders with probability (close to) zero ."

This is a difficult prescription to elude. But in fact it is not clear whethercurbing or eliminating evasion is always a desirable goal. In general terms, thedesirability of perfect enforcement is tied to the "goodness" of the tax to beenforced. For instance, when perfect enforcement of income tax would result inthe collapse of the taxed activity, one may well ask whether such unbearableburden represents the right policy.

Even if perfect enforcement were theoretically beneficial, however, it wouldnot be likely to be cost free, as suggested by the Draconian rule. For instance,when adjudication is not perfect and innocent individuals can be convicted,infinite sanctions may entail very high welfare costs. Also, when individualsmay engage in activities to avoid conviction, the social cost of enforcement mayincrease with the penalty [ Malik (1990) ].

From a practical point of view, the major impediment to infinite fines derivesfrom taxpayers' limited wealth. Since convicted evaders cannot be forced tolabor, they will be able to foot a penalty at most as great as their own wealth. TheDraconian rule thus needs to be rephrased as follows: when strict enforcementis desirable, the optimal penalty is that which expropriates the taxpayer of all hiswealth.

Enforcement policies, however, can be much more sophisticated than thecombination of two variables, the penalty and the audit rate. The auditprobability itself, for instance, need not be the same for all taxpayers. Indeed, asimple way of making audit strategy more effective is to base it on informationspecific to the taxpayer, which may include any observable characteristiccorrelated with real tax liability, from compliance records to consumptionpatterns. Clearly, the relation of an individual's reported tax liability to theaverage for similar taxpayers may then become the key to singling outcandidates for auditing.

In an important article, Reinganum and Wilde (1985) prove that by makingaudits conditional on the level of reported liability, the enforcer can increase netrevenue. They analyze a simple cut-off rule, whereby an audit is triggered if andonly if reported income is "too low". They show that this rule dominates therandom audit rule considered by Allingham and Sandmo, and that it is the mosteconomical way to foster truthful reporting when taxpayers are risk-neutral andtaxes and fines are lump-sum. Scotchmer (1987) and Sanchez and Sobel (1993) extend this result, proving that the cut-off audit rule is the optimal policy for anet revenue-maximizing enforcer when taxes and fines are proportional andtaxpayers are risk-neutral. These findings prompt the following observations.First, cost-efficient enforcement requires that audits be used primarily as adeterrent rather than as a means to collect fines. Their function is to fostercorrect self-reporting by individuals. Indeed, under the optimal policy audits willbe performed only on people who are found (ex-post) to be honest - hence nofines will ever be collected. Second, the optimal cut-off level is strictly dependenton the distribution of income among the population: effective auditing requiresreliable information on taxpayers' expected liability. Finally, optimal enforcementis likely to induce a strong regressive bias, as it provides high-income taxpayerswith better chances to evade than low-income taxpayers. The idea is thathigh-income individuals have greater opportunities to misreport, and since it ismore costly to dissuade them from evading, one should let them off the hook [onthis, see also Scotchmer (1992) ]. This problem may be alleviated by shapingaudit policy according to indexes correlated with true income [Scotchmer (1987)] and, to a lesser extent, by suitably adjusting the tax rate [ Cremer, Marchand andPestieau (1990) ].

These considerations indicate that simple models in the Allingham andSandmo mold are not adequate to the problematic issues underlying the designof an effective enforcement policy. The matter becomes still more complex whenone considers the interrelation between optimal enforcement and optimaltaxation.

The so-called "principal-agent" approach to enforcement discussed in theforegoing paragraphs constitutes one of the most general frameworks foranalyzing tax evasion and its relation to public policy. The main pitfall is itsextremely demanding assumptions concerning the enforcer's ability to deviseand execute the optimal policy. Indeed, one may argue that actual tax enforcersdo not always possess the features that would qualify them as "rational." Likeother branches of the public administration, they often have conflicting orill-defined incentives, they may be governed by "process" rather than"outcome" oriented rules, and they are likely to have short-sighted and perhapsmultiple goals. This suggests that the enforcer may tend to act myopically andjust "react" to impulses from the economic system. Thus the enforcer maydecide auditing policy taking the amount of evasion in the economy as givenand aiming to maximize detection, disregarding deterrence. This view, based onthe assumption that the tax enforcer cannot credibly precommit to any specificauditing policy, is forcefully advanced by Graetz, Reinganum and Wilde (1986) and Reinganum and Wilde (1991) . Their argument is that since actual audit ratesare not observed by taxpayers, the enforcer has an incentive to relax anyannounced auditing policy once taxpayers have reported their incomes, i.e. afterthe policy has performed its deterrent effect. Since taxpayers will anticipate theenforcer's ex-post deviation, they will not rely on the announced policy and willengage in greater evasion. The bottom line is that, in equilibrium, audits will beperformed on likely evaders rather than on compliant (i.e. deterred) taxpayers.This would appear to be a most reasonable prediction, and it tallies with actualenforcement practices.

The comparative statics of the no-commitment model differ in nature fromthose of commitment models. With no-commitment, the evasion rate and theaudit rate are determined simultaneously, whereas under commitment the auditrate determines the evasion rate. Consider, for instance, the effect of an increasein the audit cost. In the no-commitment model, evaders will evade more becausethey know that, caeteris paribus , the enforcer will react less harshly (due to thehigher enforcement costs). The higher evasion rate, however, rises the net returnfrom auditing and restores the enforcer's incentive to exert effort. In equilibrium,the evasion rate will increase and the audit rate will not decrease. In the modelswith commitment, an increase in the audit cost means that audits become a moreexpensive deterrent tool. The enforcer will hence use them more parsimoniouslyand evasion rate will increase. In contrast to the no-commitment model, theequilibrium audit rate will decrease.

The two types of model provide different insights on tax enforcement."Principal-agent" models (with commitment) are probably best used to define theconstraints that tax evasion puts on the effective tax system. They neatly definethe set of implementable allocations on the assumption that the enforcerperforms at maximum capacity. The "no-commitment" approach, with a lowerprofile, aims at capturing a version of tax enforcement closer to actual practice.On the whole, however, these models still provide a very "stylized" view ofenforcement practice. They focus on just two enforcement tools, i.e. the penaltyand the audit probabilities, and ignore most of the institutional features of realenforcement.

It is clear by now that real compliance decisions are much more complex thanthose depicted by standard economic models, in that taxpayers are subject to awide variety of sociological and ethical factors. Nor is even the effect ofenforcement policy itself fully captured by standard models. Real enforcementis unquestionably more than a mere combination of penalty and auditprobabilities (regardless of how sophisticated these can be made). The processthat leads from the checking of tax returns to the conviction of evaders islengthy and complex, perhaps involving various bodies (tax administration, taxcourts) and procedures (interviews, cross-examinations, settlements, etc.). Theshape of the prosecution process affects taxpayers' attitudes towardscompliance in two ways. First, it determines the actual probability that a sanctionwill be imposed on evaders and, possibly, innocent taxpayers; and second, itmay affect the degree of "hostility" in the taxpayer's perception of the taxsystem.

In a word, institutional and procedural features matter. They impose costs ontaxpayers and affect the outcome of the prosecution process. We will touchbriefly on some of these aspects, starting with the costs.

According to a number of studies, the cost to the taxpayer of compliancewith the most common taxes (income and VAT) in industrialized countries canbe as high as 10-13% of the total tax liability [see the pioneering contribution of Sandford (1973) , as well as Sanford et al. (1981) , Slemrod (1989) , Pitt and Slemrod(1989) , Sandford, Goodwin, and Hardwick (1989) , Blumenthal and Slemrod (1992) and Sandford (1995) ]. High compliance costs, which may be due to complex taxschedules and rules, not only tilt the "cost-benefit analysis" towards evasion,but may also generate resentment, weakening taxpayers' moral conscience oreven prompting them to evade as a form of "punishment" for the taxadministration. Legislatures should accordingly avoid the vicious circle ofcountering evasion by increasing the complexity of tax regulations, which raisescompliance costs and fosters further evasion.

When the tax legislation is very complex, taxpayers usually have to turn totax experts (CPAs or tax preparers), who have great power to influence theirclients' attitudes towards evasion, thanks to their superior knowledge ofenforcement patterns. An interesting empirical study by Klepper and Nagin(1989b) on the United States suggests that tax preparers encourage compliancewith regard to unequivocal items, and discourage it with regard to ambiguousones. [Other investigations of this issue can be found in Scotchmer (1989) , Reinganum and Wilde (1991) , Erard (1993) and Franzoni (1998) .]

Costs are also entailed in mandatory record-keeping and reporting, whoserole is to increase the visibility of offenses, i.e. the "frequency and ease withwhich they come to the attention of and can be proved by enforcement officials"[ Kagan (1989) ]. As noted in section 3, noncompliance varies greatly witheconomic grouping, as tax violation by different groups has different degrees of"visibility." Unsurprisingly, therefore, evasion is apparently most commonamong independent contractors, professionals, and farmers. Conversely,compliance is highest among payroll employees subject to withholding.

In a technical sense, higher visibility makes it easier both to "observe" thereal situation or behavior of the taxpayer (by signaling potential violations) andto "verify" it (prove it in court). Some forms of mandatory record-keeping, forexample, serve a legal evidentiary function, implying a de facto shift in theburden of proof. It is the taxpayer who has to prove his compliance with the law,and bear the costs thereof. The question of the optimal amount of complianceduties to impose on taxpayers is therefore bound up with the optimal allocationof the burden of proof. Generally, the efficient allocation is that which places theonus of the proof on the party for which it is least costly (given its level ofinformativeness).

Another important factor in the "visibility" of tax law violations is thestandard of proof. Indeed, the difference between the "observability" and the"verifiability" of the tax base is precisely defined by the type of evidence thatis necessary to asses it legally (and possibly prove that the original paymentswere not correct). In most countries, tax authorities have the power to estimatetaxpayer's liability by discretionary means when the information supplied by thetaxpayer is deemed insufficient or clearly incorrect [ OECD (1990) ]. Clearly, underthese circumstances the standard of proof can be rather lax, and the use of merestatistical evidence can be used to prove taxpayers' obligations. Presumptivetaxation is a case in which statistical estimates and proxies are used ab origine to define the tax obligation, resulting in the automatic visibility of the activitiescovered and imposing virtually no compliance costs on taxpayers [see Tanzi(1991) ]. Note that simplifications and reductions in compliance costs willordinarily be achieved only at the expense of reduced ability to discriminateamong taxpayers (for purposes of either vertical or horizontal equity). As ispointed out by Kaplow (1996) , a trade-off is likely to arise between containingcompliance costs and accuracy in liability assessment.

On the procedural side, another important consideration is the possibility ofresolving disputes through amicable settlements between taxpayers and theadministration. In most countries, taxpayers can make a "deal" with inspectorsand obtain substantial penalty discounts in exchange for collaboration [ OECD(1990) ]. When deals are left to the discretion of the revenue service, enforcementis likely to be adversely affected. Discretionary deals not only reduce theadministration's ability to precommit itself to any specific enforcement policy butmay also foster opportunism, tempting the administration to increase itsinefficiencies (e.g. lengthy and invasive prosecution procedures) so as toincrease its "take" at the settlement stage [ Franzoni (1995) ]. Tax amnesties,though sharing some of these problems, may prove desirable, as they offertaxpayers social insurance against unexpected shocks, allowing them tocomplete their payments after uncertainty (about their income or their truepreferences) has been resolved [ Andreoni (1991) , Malik and Schwab (1991) ].

A fundamental problem in considering the optimal institutional design of taxenforcement relates to incentives for enforcers. More fundamentally, thequestion is whether enforcement should be the job of public or private agents.First raised in general terms by Becker and Stigler (1974) , the issue has beenexamined in the specific context of tax evasion by several authors. While in mostcountries taxes are collected by a public agency, in a few cases (as with importduties in Indonesia) collection is delegated to private contractors. Melumad andMookherjee (1989) show that delegation of tax enforcement to a private partymay be viable (i.e., it can replicate the full-commitment solution) if it is backed byan incentive scheme based on publicly observable aggregate variables (auditexpenditure, taxes filed and fines collected). This scheme rewards the agent forcollecting fines, or, when no fine is collected, for meeting the target auditbudget. Toma and Toma (1992) observe that different institutional arrangementsmay entail different agency costs so that depending on their incidence eitherpublic or private enforcement may be desirable.

A key agency cost is that associated with the danger of corruption. Since thepersonal aim of enforcement officers may not correspond to institutionalpurposes, there is scope for collusion with taxpayers. This seriously complicatesthe analysis, as a third constraint (no collusion) must now be taken into account.For while it may be contended that combating corruption can help control taxevasion, it may well be that anti-evasion measures as such ultimately justincrease the scope and the extent of corruption [see Chu (1990) , Chander andWilde (1992a) , Besley and McLaren (1993) , Mookherjee and Png (1995) , Flattersand McLoad (1995) , Hindriks, Keen and Muthoo (1996) ]. This confirms that theinstitutional features of the enforcement system represent a point of fundamentalimportance. These features define the incentive structure governing the conductof enforcers and crucially affect the actual functioning of all enforcement tools.

The foregoing offers an analytical framework for treating some salient aspectsof tax noncompliance, suggesting causes and possible remedies. As must beclear by now, tax evasion is a complex phenomenon that cannot be eradicatedby marginal changes in enforcement practice. Social and moral attitudes, whichplay a very important role, are very slow to change and are often beyond thereach of public policy. Standard enforcement therefore remains crucial. Theempirical evidence suggests that a stricter enforcement regime is likely to inducegreater compliance; the key variable here is the probability of detection.

To date, most studies in this field have focused on two enforcement tools:penalty rates and auditing probabilities. Much work remains to be done toascertain the impact on compliance of less striking but nonetheless importantprocedural and institutional factors.

Actually, closer examination of institutional reality suggests that the auditrate may not be the relevant variable. What really matters is the probability thatan investigation will eventually result in conviction and sanction for thewrongdoer. Here a host of additional factors come into play: whether evasionleaves detectable traces, the specific ability and expertise of the auditors, the setof investigative tools at their disposal (e.g. the degree of banking secrecy), thepossibility of inducing taxpayer collaboration, the feasibility of out-of-courtsettlements, the standard of proof, the definition of "fault," the clarity of the taxlaw, the number of levels of appeal, and so on.

Research into the impact that these procedural aspects have on taxpayercompliance is still in its infancy. Better integration of the research on tax evasionwith the "law and economics" analysis of legal rules is definitely desirable. Astheoretical analysis proceeds, additional empirical work will be needed togetherwith more extensive study of comparative tax enforcement law and procedure.

Benjamini, Yael and Maital, Shlomo (1985) , 'Optimal Tax Evasion and Optimal TaxEvasion Policy: Behavioral Aspects', in Gaertner, Wulf and Wenig, Alois (eds.), TheEconomics of the Shadow Economy: Proceedings of th International Conference on theEconomics of the Shadow Economy Held at the University of Bielefeld, West Germany,October 10-14, 1983 , Berlin, Springer, 245-264.

Cowell, Frank A. (1985), 'Public Policy and Tax Evasion: Some Problems', in Gaertner,Wulf and Wenig, Alois (eds.), The Economics of the Shadow Economy: Proceedings ofth International Conference on the Economics of the Shadow Economy Held at theUniversity of Bielefeld, West Germany, October 10-14, 1983 , Berlin, Springer, 273-284.

Hansson, Ingemar (1985) , 'Tax Evasion and Government Policy', in Gaertner, Wulf andWenig, Alois (eds.), The Economics of the Shadow Economy: Proceedings of thInternational Conference on the Economics of the Shadow Economy Held at theUniversity of Bielefeld, West Germany, October 10-14, 1983 , Berlin, Springer, 285-300.

Holland, Daniel M. (1984) , 'Measuring and Combatting Income Tax Evasion', in Hanusch,Horst (ed.), Public Finance and the Quest for Efficiency: Proceedings of the 38thCongress of the International Institute of Public Finance, Copenhagen , Detroit, WayneState University Press, 329-348.

Isachsen, Arne Jon, Samuelson, S.S. and Strom, Steinar (1985) , 'The Behavior of TaxEvaders', in Gaertner, Wulf and Wenig, Alois (eds.), The Economics of the ShadowEconomy: Proceedings of th International Conference on the Economics of the ShadowEconomy Held at the University of Bielefeld, West Germany, October 10-14, 1983 ,Berlin, Springer.

Stroope, John C. (1988) , An Empirical Analysis of the Impact of ERTA and TEFRA on TaxCompliance , Pennsylvania Economic Association. Proceedings of the Third AnnualMeeting, May 27 and 28, 1988. University Park: Pennsylvania State University.